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as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous
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A notable property of the mandelbox, particularly for scale −1.5, is that it contains approximations of many well known fractals within it.
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Please help improve this article by looking for better, more reliable sources. Unreliable citations may be challenged and removed.
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689:. Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications. Vol. 06. World Scientific.
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Then, depending on the magnitude of the vector, change its magnitude using some fixed values and a specified
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with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous
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The simple definition of the mandelbox is this: repeatedly transform a vector
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component > 1: component := 2 - component
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component < -1: component := -2 - component
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610:{\displaystyle 4\cdot {\frac {{\text{scale}}+1}{{\text{scale}}-1}}}
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Viewpoints: Mathematical
Perspective and Fractal Geometry in Art
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792:"Patterns of Visual Math – Mandelbox, tglad, Amazing Box"
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the mandelbox contains a solid core. Consequently, its
557:{\displaystyle 1<{\text{scale}}\leq 4{\sqrt {n}}+1}
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2836:The Drawing of Geometric Patterns in Saracenic Art
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2971:Goudreau Museum of Mathematics in Art and Science
735:French National Centre for Scientific Research
3092:
2966:European Society for Mathematics and the Arts
2140:Mathematica: A World of Numbers... and Beyond
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301:is greater than 1, subtract it from 2; or if
8:
2120:List of works designed with the golden ratio
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53:Learn how and when to remove these messages
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2180:Cathedral of Saint Mary of the Assumption
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221:Learn how and when to remove this message
203:Learn how and when to remove this message
150:Learn how and when to remove this message
2726:Vier Bücher von Menschlicher Proportion
1774:List of fractals by Hausdorff dimension
841:Video : zoom in the Mandelbox cube
648:
297:(which corresponds to a dimension), if
724:
722:
86:Please improve this article by adding
731:"Mandelbox. Images des Mathématiques"
305:is less than -1, subtract it from −2.
7:
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3051:
756:"Negative 1.5 Mandelbox – Mandelbox"
510:{\displaystyle {\text{scale}}<-1}
285:, according to the following rules:
2911:Journal of Mathematics and the Arts
794:. February 13, 2011. Archived from
3071:. You can help Knowledge (XXG) by
2925:Making Mathematics with Needlework
412:is the constant being tested, and
14:
2751:I quattro libri dell'architettura
1756:How Long Is the Coast of Britain?
34:This article has multiple issues.
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2275:Self-portrait in a Convex Mirror
1959:
321:The iteration applies to vector
166:
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42:or discuss these issues on the
2986:National Museum of Mathematics
2738:Regole generali d'architettura
1780:The Fractal Geometry of Nature
836:Images of some Mandelbox cubes
451:
441:
1:
88:secondary or tertiary sources
2511:Garden of Cosmic Speculation
774:"More negatives – Mandelbox"
16:Fractal with a boxlike shape
3123:Mathematical analysis stubs
1796:Chaos: Making a New Science
3144:
3050:
2028:Islamic geometric patterns
1169:Mathematical visualization
1144:Computer-generated imagery
289:First, for each component
3025:
2849:A Mathematician's Apology
1957:
1182:
883:
729:Leys, Jos (27 May 2010).
2961:The Bridges Organization
1164:Iterated function system
686:Exploring Scale Symmetry
253:A "scale -1.5" Mandelbox
2823:The Grammar of Ornament
2775:Nature's Harmonic Unity
2685:De prospectiva pingendi
831:Gallery and description
175:Some of this article's
3067:–related article is a
2976:Institute For Figuring
2888:The 'Life' of a Carpet
2713:A Treatise on Painting
1788:The Beauty of Fractals
658:"What Is A Mandelbox?"
611:
558:
511:
465:
254:
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75:relies excessively on
2857:George David Birkhoff
2831:Ernest Hanbury Hankin
2699:De divina proportione
2679:Piero della Francesca
2658:Leon Battista Alberti
2245:Piero della Francesca
1884:Hyperboloid structure
798:on February 13, 2011.
683:Lowe, Thomas (2021).
612:
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512:
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252:
245:A "scale-3" Mandelbox
244:
237:A "scale-2" Mandelbox
236:
2782:Frederik Macody Lund
2653:Filippo Brunelleschi
2534:Hamid Naderi Yeganeh
2396:La condition humaine
1734:Lewis Fry Richardson
1729:Hamid Naderi Yeganeh
1519:Burning Ship fractal
1451:Weierstrass function
1103:Burning Ship fractal
568:
521:
490:
479:when generalised to
431:
257:In mathematics, the
3007:Mathematical beauty
2932:Rhythm of Structure
2875:Gödel, Escher, Bach
2671:De re aedificatoria
2302:The Ancient of Days
1921:Projective geometry
1850:Mathematics and art
1492:Space-filling curve
1469:Multifractal system
1352:Space-filling curve
1337:Sierpinski triangle
1149:Fractal compression
1072:MojoWorld Generator
1034:Wolfram Mathematica
814:"The Mandelbox Set"
3128:Chaos theory stubs
3012:Patterns in nature
2869:Douglas Hofstadter
2495:Desmond Paul Henry
2485:Bathsheba Grossman
2417:The Swallow's Tail
2338:Giorgio de Chirico
2210:Sydney Opera House
2065:Croatian interlace
1719:Aleksandr Lyapunov
1699:Desmond Paul Henry
1663:Self-avoiding walk
1658:Percolation theory
1302:Iterated function
1243:Fractal dimensions
637:Lichtenberg figure
607:
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416:is a real number.
362:< 0.5:
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2862:Aesthetic Measure
2733:Sebastiano Serlio
2707:Leonardo da Vinci
2597:
2596:
2589:Margaret Wertheim
2250:Leonardo da Vinci
1816:
1815:
1762:Coastline paradox
1739:Wacław Sierpiński
1724:Benoit Mandelbrot
1648:Fractal landscape
1556:Misiurewicz point
1461:Strange attractor
1342:Apollonian gasket
1332:Sierpinski carpet
1195:
1194:
1154:Fractal landscape
1064:Scenery generator
1058:
1057:
893:Graphics software
704:978-981-3278-55-4
664:on 8 October 2016
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564:they have length
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277:Simple definition
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2574:Hiroshi Sugimoto
2524:Robert Longhurst
2470:Helaman Ferguson
2425:Crockett Johnson
2354:Circle Limit III
2323:Danseuse au café
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2200:Pyramid of Khufu
1963:
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1679:Michael Barnsley
1546:Lyapunov fractal
1404:Sierpiński curve
1357:Blancmange curve
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929:Kalles Fraktaler
877:Fractal software
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2745:Andrea Palladio
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3002:Droste effect
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2981:Mathemalchemy
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2918:Lumen Naturae
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2564:Reza Sarhangi
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2475:Peter Forakis
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2390:René Magritte
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2361:Print Gallery
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2330:L'Oiseau bleu
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2256:Vitruvian Man
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2240:Paolo Uccello
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2161:Pi in the Sky
2158:
2156:
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2151:
2149:
2148:
2144:
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2141:
2137:
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2134:
2133:Mathemalchemy
2130:
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2019:
2016:
2014:
2011:
2009:
2006:
2002:
2001:Vastu shastra
1999:
1997:
1994:
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1991:Geodesic dome
1989:
1988:
1987:
1984:
1982:
1979:
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1947:
1944:
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1930:
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1924:
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1916:Plastic ratio
1914:
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1904:Camera lucida
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1636:Brownian tree
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1564:
1563:Multibrot set
1561:
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1540:
1539:Douady rabbit
1537:
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1419:
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1410:
1409:Z-order curve
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1385:
1382:
1380:
1379:Hilbert curve
1377:
1375:
1372:
1368:
1365:
1364:
1363:
1362:De Rham curve
1360:
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1355:
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1353:
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1328:
1327:Menger sponge
1325:
1323:
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1318:
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1312:Barnsley fern
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1188:
1185:
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1162:
1160:
1159:Fractal flame
1157:
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1126:
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1096:Found objects
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1035:
1032:
1030:
1029:Ultra Fractal
1027:
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1017:
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998:
992:
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769:
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748:
736:
733:(in French).
732:
725:
723:
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714:
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706:
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696:
695:10.1142/11219
692:
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411:
405:
401:
397:
393:
389:
385:
381:
377:
374:magnitude of
373:
369:
365:
361:
358:magnitude of
357:
353:
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196:
193:December 2023
184:
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143:
140:December 2023
132:
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118:
115:
111:
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104:
101: –
100:
96:
95:Find sources:
89:
83:
82:
78:
73:This article
71:
67:
62:
61:
56:
54:
47:
46:
41:
40:
35:
30:
21:
20:
3073:expanding it
3062:
3047:
3034:
2937:
2930:
2923:
2916:
2909:
2903:Publications
2887:
2873:
2861:
2847:
2835:
2821:
2798:
2794:Jay Hambidge
2787:Ad Quadratum
2786:
2774:
2749:
2737:
2725:
2711:
2697:
2693:Luca Pacioli
2683:
2669:
2662:
2632:
2620:
2544:Hinke Osinga
2539:István Orosz
2509:
2500:Anthony Hill
2455:Scott Draves
2450:Erik Demaine
2434:Contemporary
2415:
2408:
2394:
2380:
2373:
2366:
2359:
2352:
2348:M. C. Escher
2328:
2321:
2307:
2300:
2273:
2269:Parmigianino
2254:
2185:Hagia Sophia
2159:
2152:
2145:
2138:
2131:
2124:
2008:Computer art
1986:Architecture
1946:Tessellation
1929:Architecture
1879:Golden ratio
1808:Chaos theory
1803:Kaleidoscope
1794:
1786:
1778:
1704:Gaston Julia
1684:Georg Cantor
1577:
1509:Escape-time
1441:Gosper curve
1389:Lévy C curve
1374:Dragon curve
1253:Box-counting
1117:
1043:Windows only
812:Chen, Rudi.
796:the original
786:
777:
768:
759:
750:
738:. Retrieved
685:
678:
666:. Retrieved
662:the original
651:
485:
483:dimensions.
480:
476:
426:
423:
413:
409:
407:
403:
399:
395:
391:
387:
383:
379:
375:
371:
367:
363:
359:
355:
351:
347:
343:
340:
336:
332:
328:
325:as follows:
322:
320:
309:
302:
298:
294:
290:
282:
280:
258:
256:
217:
199:
190:
179:
146:
137:
127:
120:
113:
106:
94:
74:
50:
43:
37:
36:Please help
33:
2843:G. H. Hardy
2646:Renaissance
2616:Polykleitos
2554:Tony Robbin
2465:John Ernest
2460:Jan Dibbets
2410:Crucifixion
2233:Renaissance
2087:Mathematics
2060:Celtic knot
2023:Fractal art
1925:Proportion
1899:Perspective
1799:(1987 book)
1791:(1986 book)
1783:(1982 book)
1769:Fractal art
1689:Bill Gosper
1653:Lévy flight
1399:Peano curve
1394:Moore curve
1280:Topological
1265:Correlation
907:Open-source
898:Fractal art
888:Digital art
740:18 December
668:15 November
656:Lowe, Tom.
180:may not be
99:"Mandelbox"
3112:Categories
2817:Owen Jones
2664:De pictura
2569:Oliver Sin
2519:Andy Lomas
2368:Relativity
2099:String art
2013:Fiber arts
1894:Paraboloid
1607:Orbit trap
1602:Buddhabrot
1595:techniques
1583:Mandelbulb
1384:Koch curve
1317:Cantor set
1174:Orbit trap
1128:Mandelbulb
643:References
632:Buddhabrot
627:Mandelbulb
420:Properties
346::
339:component
317:Generation
271:Julia sets
110:newspapers
77:references
39:improve it
2628:Vitruvius
2602:Theorists
2382:Waterfall
2287:19th–20th
2215:Taj Mahal
2195:Parthenon
2172:Buildings
2126:Continuum
2094:Sculpture
2070:Interlace
1864:Algorithm
1714:Paul Lévy
1593:Rendering
1578:Mandelbox
1524:Julia set
1436:Hexaflake
1367:Minkowski
1287:Recursion
1270:Hausdorff
1118:Mandelbox
1113:Julia set
914:Apophysis
713:224939666
599:−
575:⋅
536:≤
502:−
475:is 3, or
394: :=
382: :=
366: :=
259:mandelbox
45:talk page
3118:Fractals
3036:Category
2763:Romantic
2441:Max Bill
2375:Reptiles
2190:Pantheon
2147:Octacube
2113:Artworks
2055:Knotting
2043:Muqarnas
1941:Symmetry
1869:Catenary
1857:Concepts
1624:fractals
1511:fractals
1479:L-system
1421:T-square
1229:Fractals
1187:Category
1087:VistaPro
1082:Terragen
1019:Chaotica
986:Fractint
979:Freeware
965:openPlaG
939:Sterling
934:MilkDrop
621:See also
390:)^2
370:* 4
337:for each
331:iterate(
329:function
182:reliable
3065:fractal
2995:Related
2609:Ancient
2343:Man Ray
2289:Century
2225:Artists
2082:Origami
1996:Pyramid
1874:Fractal
1573:Tricorn
1426:n-flake
1275:Packing
1258:Higuchi
1248:Assouad
1137:Related
1077:Picogen
991:IFStile
919:Blender
372:else if
352:else if
335:):
312:factor.
263:fractal
124:scholar
2810:Modern
2446:Martin
2309:Newton
2104:Tiling
2048:Zellij
2018:4D art
1672:People
1622:Random
1529:Filled
1497:H tree
1416:String
1304:system
1050:VisSim
1000:Retail
711:
701:
408:Here,
126:
119:
112:
105:
97:
3063:This
2621:Canon
2077:Music
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